在一般场和具有光滑或粗糙壁的任意形状测量池中捕获自旋1/2粒子的电偶极搜索中的几何相位
Geometric phases in electric dipole searches with trapped spin-1/2 particles in general fields and measurement cells of arbitrary shape with smooth or rough walls
摘要：
几何相位在利用拉姆齐分离振荡场核磁共振寻找中子的永久电偶极矩中的重要作用首先由康明斯提出，并由彭德伯里等人详细研究。他们的分析基于布洛赫方程。在随后的工作中，使用自旋密度矩阵Lamoreaux和Golub显示之间的关系的频率偏移和关联函数的领域所看到的被困粒子在一般领域（雷德菲尔德理论）。最近，我们提出了一个解决方案的薛定谔方程的自旋$1/2$粒子在圆柱形陷阱与光滑的墙壁和暴露于任意领域[Steyerl等。]在这里，我们扩展这项工作，以显示如何Redfield理论遵循直接从薛定谔方程的解决方案。这有助于突出Redfield理论的有效性条件，这是文献中大量讨论的主题[例如，Nicholas等人]我们的结果可以应用在Redfield结果不再成立的地方，如观测时间的顺序或短于相关时间和非随机系统，因此我们可以说明瞬态自旋动力学，即随着时间的推移逐渐发展的位移开始后的自由进动。我们考虑系统的粗糙，漫反射壁，圆柱形陷阱的几何形状与任意截面，和场扰动不，在移动粒子的框架，平均为零的时间。我们通过直接的、详细的计算表明，对于镜面反射壁的矩形单元和漫反射壁的圆形单元，薛定谔方程的结果与Redfield理论的结果是一致的。
英文摘要：
The important role of geometric phases in searches for a permanent electric dipole moment of the neutron, using Ramsey separated oscillatory field nuclear magnetic resonance, was first noted by Commins and investigated in detail by Pendlebury et al. Their analysis was based on the Bloch equations. In subsequent work using the spin density matrix Lamoreaux and Golub showed the relation between the frequency shifts and the correlation functions of the fields seen by trapped particles in general fields (Redfield theory). More recently we presented a solution of the Schrödinger equation for spin-$1/2$ particles in circular cylindrical traps with smooth walls and exposed to arbitrary fields [Steyerl et al.] Here we extend this work to show how the Redfield theory follows directly from the Schrödinger equation solution. This serves to highlight the conditions of validity of the Redfield theory, a subject of considerable discussion in the literature [e.g., Nicholas et al.] Our results can be applied where the Redfield result no longer holds, such as observation times on the order of or shorter than the correlation time and non-stochastic systems and thus we can illustrate the transient spin dynamics, i.e. the gradual development of the shift with increasing time subsequent to the start of the free precession. We consider systems with rough, diffuse reflecting walls, cylindrical trap geometry with arbitrary cross section, and field perturbations that do not, in the frame of the moving particles, average to zero in time. We show by direct, detailed, calculation the agreement of the results from the Schrödinger equation with the Redfield theory for the cases of a rectangular cell with specular walls and of a circular cell with diffuse reflecting walls.
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